NTA JEE Main 8th April2023 Shift 1

A cylindrical wire of mass $$(0.4 \pm 0.01)$$ g has length $$(8 \pm 0.04)$$ cm and radius $$(6 \pm 0.03)$$ mm. The maximum error in its density will be

Two forces having magnitude A and $$\dfrac{A}{2}$$ are perpendicular to each other. The magnitude of their resultant is:

Dimension of $$\dfrac{1}{\mu_0 \varepsilon_0}$$ should be equal to

Two projectiles A and B are thrown with initial velocities of 40 m s$$^{-1}$$ and 60 m s$$^{-1}$$ at angles 30° and 60° with the horizontal respectively. The ratio of their ranges respectively is $$(g = 10$$ m s$$^{-2}$$)

At any instant the velocity of a particle of mass 500 g is $$(2t\hat{i} + 3t^2\hat{j})$$ m s$$^{-1}$$. If the force acting on the particle at $$t = 1$$ s is $$(\hat{i} + x\hat{j})$$ N. Then the value of $$x$$ will be:

Given below are two statements:
Statement I: If $$E$$ be the total energy of a satellite moving around the earth, then its potential energy will be $$\dfrac{E}{2}$$.
Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy $$E$$.
In the light of the above statements, choose the most appropriate answer from the options given below.

The weight of a body on the earth is 400 N. Then weight of the body when taken to a depth half of the radius of the earth will be:

An aluminium rod with Young's modulus $$Y = 7.0 \times 10^{10}$$ N m$$^{-2}$$ undergoes elastic strain of 0.04%. The energy per unit volume stored in the rod in SI unit

An air bubble of volume 1 cm$$^3$$ rises from the bottom of a lake 40 m deep to the surface at a temperature of 12°C. The atmospheric pressure is $$1 \times 10^5$$ Pa, the density of water is 1000 kg m$$^{-3}$$ and $$g = 10$$ m s$$^{-2}$$. There is no difference of the temperature of water at the depth of 40 m and on the surface. The volume of air bubble when it reaches the surface will be

Given below are two statements:
Statement I: If heat is added to a system, its temperature must increase.
Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.
In the light of the above statements, choose the correct answer from the options given below